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2007 An uncountably infinite number of indecomposable totally reflexive modules
Ryo Takahashi
Nagoya Math. J. 187: 35-48 (2007).

Abstract

Several years ago, Huneke and Leuschke proved a theorem solving a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type which is complete or has uncountable residue field has at most a one-dimensional singular locus. In this paper, it is verified that the assumption of the excellent property can be removed, and the theorem is considered over an arbitrary local ring. The main purpose of this paper is to prove that the existence of a certain prime ideal and a certain totally reflexive module implies the existence of an uncountably infinite number of isomorphism classes of indecomposable totally reflexive modules.

Citation

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Ryo Takahashi. "An uncountably infinite number of indecomposable totally reflexive modules." Nagoya Math. J. 187 35 - 48, 2007.

Information

Published: 2007
First available in Project Euclid: 4 September 2007

zbMATH: 1129.13013
MathSciNet: MR2354554

Subjects:
Primary: 13C14 , 16G60

Keywords: Cohen-Macaulay ring , Countable Cohen-Macaulay type , semidualizing , Totally reflexive

Rights: Copyright © 2007 Editorial Board, Nagoya Mathematical Journal

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